Constrained CMIP6 projections indicate less warming and a slower increase in water availability across Asia

Climate projections are essential for decision-making but contain non-negligible uncertainty. To reduce projection uncertainty over Asia, where half the world’s population resides, we develop emergent constraint relationships between simulated temperature (1970–2014) and precipitation (2015–2100) growth rates using 27 CMIP6 models under four Shared Socioeconomic Pathways. Here we show that, with uncertainty successfully narrowed by 12.1–31.0%, constrained future precipitation growth rates are 0.39 ± 0.18 mm year−1 (29.36 mm °C−1, SSP126), 0.70 ± 0.22 mm year−1 (20.03 mm °C−1, SSP245), 1.10 ± 0.33 mm year−1 (17.96 mm °C−1, SSP370) and 1.42 ± 0.35 mm year−1 (17.28 mm °C−1, SSP585), indicating overestimates of 6.0–14.0% by the raw CMIP6 models. Accordingly, future temperature and total evaporation growth rates are also overestimated by 3.4–11.6% and −2.1–13.0%, respectively. The slower warming implies a lower snow cover loss rate by 10.5–40.2%. Overall, we find the projected increase in future water availability is overestimated by CMIP6 over Asia.

3. Line 64-65: The authors mentioned CMIP6 models reduced temperature bias compared to the CMIP5 models. However, CMIP6 models simulated precipitation better than CMIP5 models (See Figure S1b vs. Figure 1b). Why? 4. Line 132: What is EC? Does it mean the emergent constraint? Then use the full name. 5. In Supplementary Figures. 2-4, some regions have a negative relationship between temperature and precipitation (e.g., Pakistan and Indonesia). The authors should clarify whether such regions were included in the analysis or not. 6. Line 225-227: In Figure 3b,d,f, inter-model uncertainties decreased effectively after the emergent constraint. However, the minimum values of inter-model uncertainties of temperature and evaporation did not significantly change after the emergent constraint (Figure 3b, d). In case of the snow cover, the opposite occurred. Maybe only certain CMIP6 models are sensitive to the emergent constraint, resulting in these results. Therefore, the authors should investigate the sensitivity of each model to the emergent constraint. 7. Line 228-239: There are some snow-free regions in Asia (e.g., Southeast Asia near the equator), so the analysis region should narrow down when you calculate the relationship between snow cover fraction and temperature.
Reviewer #2 (Remarks to the Author): Review for the paper entitled "Constrained CMIP6 projections indicate slower warming rates and reduced water availability across Asia" The paper is well written and clear on the results. The methodology is explained in detail with all information needed. The findings are significant and seem supported by the figures, but I have a main major concern about their interpretation. Most of the emergent constraint signal is claimed to be related to precipitation feedback on temperatures. However by reading the picture my first conclusion would be that models warming the most also see the largest increase in precipitation simply because of thermodynamics laws (higher temperature = more evaporative world). For me it's not really clear that there is a feedback here. Maybe one thing to do would be to express the precipitation change per °C (instead of per year).
That's my only major concern about the paper but I think it really needs to be clarified (either by clearly showing how it's a feedback and not just thermodynamics, or by rephrasing the text and discussion around thermodynamics considerations). It would probably not change the main results (the relation between model warming the most and having more precipitation would still be the same), but it must be clear why it is so.

Some other suggestions:
Line 65: "Asia" domain should be defined here maybe? L70: "Asian precipitation": do you consider yearly precip or only during the summer monsoon? L137-143: Maybe a K-S test (or other) could be used to see how significant is the shift between pdf? L164-170: It's not surprising to see a relationship between longwave and temperature, because longwave is basically temperature. Maybe you could look at the latent heat fluxes here too, which is more related to evaporation/precipitation. L191-195: Instead of constraining the future temperatures based on a constrained precipitation why not simply simply constrain future T based on historical T? With a similar approach done by Chai et al. (2021) for the Amazon dieback, this manuscript investigated historical temperature and precipitation trends in Asia by CMIP6 models against the observations, and used the results to adjust future projections. As CMIP6 models overestimate historical precipitation changes during 1970-2014, future precipitation projections are downgraded. However, the reviewer has some concerns. First, the emergent constraint seeks physical mechanism of a possible relationship between the two variables, but this approach will not work well in this subject, because regional precipitation is not governed by temperatures only, but also much influenced by circulation changes and associated moisture convergence. Second, the authors adjust future precipitation changes in the models in which historical temperature growth rate is large, although the ensemble mean historical temperature trend fits the observation very well. Third, after reducing the future precipitation trends, authors decrease the future temperature trends, although models had no significant bias in their historical period. The reviewer is not confident with the authors hypotheses.
Other comments (1) Methods for calculation are missing. How are different horizontal resolutions of observations and models treated? Which is the area of Asia? (2) Line 155-159: Over the Amazon, is physiological response the main reason of precipitation decrease in future, rather than an El Nino-like mean SST changes?

Responses to Reviewer #1
General comments: This study indicated slower warming and decreased water availability over Asia using CMIP6 results modified by the emergent constraint. The results of this study can be fruitful to reduce uncertainty in climate change projections over Asia. However, I can't entirely agree with the linear relationship between precipitation and temperature over Asia used in the emergent constrain method. In addition, the authors did not define the analysis region indicating Asia, where the relationship between precipitation and temperature varies depending on the area and season. Therefore, I do not recommend the publication of this manuscript until my concerns are sufficiently resolved or addressed. The details are shown below: Response: We thank the referee very much for their comments. We have addressed all the referee's suggestions, which were very valuable for improving the manuscript. In particular, we have provided further evidence, with emphasis on both the spatial differences and the inter-model differences, supporting the use of a linear relationship. Explanations of the physical mechanisms are also strengthened. The coverage of Asia has also been clearly defined, and with a new figure panel depicting the Asian-domain (in Figure 1).
Major concerns: Comment 1. The emergent constraint basically requires the linear relationship between two variables (i.e., temperature and precipitation). However, I am unsure whether there is a positive correlation between interannual variabilities of temperature and precipitation from observation. For example, more precipitation can decrease the temperature by increasing latent heat flux or increasing specific heat in land, indicating negative feedback. The authors should clarify the physical relationship between temperature and precipitation over Asia in more detail. Response: The referee raised a fundamental question whether a positive correlation exists between temperature and precipitation. To respond, we have provided additional evidence supporting this linear relationship in the revised manuscript, and further clarified the physical mechanisms over Asia in detail.
First, we collected additional observed datasets of precipitation (GPCC, 20CRv2c, HadCRUT4, GHCN, CMAP and ERA-Interim) and temperature (Delaware, HadCRUT4, GISS, NOAA), and found positive linear relationships between the historical temperature and precipitation  over Asia in all the datasets (see Supplementary Figure 4 in the revised SI and Lines 87-91 in the revised main text). To examine the correlations in detail, we randomly selected eight square areas in Asia (see Supplementary Figure 5 in the revised SI and Lines 91-94 in the revised main text), and found significant positive relationships in each of the subareas.
Second, we extracted future projections (2015-2100) of precipitation and temperature in Asia from each of the 27 CMIP6 models (see Supplementary Figure 6 in the revised SI and Lines 94-96 in the revised main text), and found consistent positive linear correlations in almost all the models under the four SSPs (the only exception is the NorESM2-LM model which exhibits poor performance in reproducing historical precipitation under SSP126 -the correlation coefficient between simulated and observed precipitation during 1970-2015 is only of 0.09, and the P value is 0.56), with high positive correlation coefficients (R ≥ 0.4 and corresponding P value<0.001) across most (82.0-92.1%) of Asia (see Supplementary Figure 7 in the revised SI and Lines 96-97 in the revised main text).
Finally, we added in-depth explanations for the physical mechanisms behind the constraint relationship as follows: As temperatures rise, evaporation from soil and open waters increases 1 , and elevated CO 2 concentrations are expected to increase vegetation transpiration through a fertilization effect, found in both observed and simulated evidence 2 . Thereby, atmospheric moisture increases with evaporation and transpiration, leading to more precipitation.
Further, under warming conditions, the water-holding capacity of the atmosphere is estimated to increase by 7% K -1 3 , using the Clausius-Clapeyron equation (Eq. R1 and the converted form, Eq. R2), which has been widely used to discuss the sensitivity of precipitation change to temperature variation all over the world, including Asia 4-5 : where q s and T are saturation specific humidity and temperature, respectively. L v is the latent heat of condensation at temperature T (assumed to be 2.5×10 6 J kg −1 ), and R v is the gas constant for water vapor (461.5 J kg −1 K −1 ). (Under the condition that the total pressure is much larger than the water vapor pressure, α is calculated to be 0.07 K −1 , i.e., q s increases by 7 % per degree of warming.) In response to the increased saturation specific humidity, precipitation is thus expected to increase, according to a thermodynamic scaling equation (Eq. R3 6 , and the converted form, Eq. R4 3 ): where Pre is precipitation, and M f is the convective mass flux. Since M f is usually assumed to be unchanged (i.e., dM f =0), precipitation is linearly dependent on temperature change. Considering that Eq. R4 is also constrained by radiative cooling, the increasing rate of precipitation is expected to be weakened by 4-6% K -1 , to about 1−3% K -1 . In agreement with this estimation, Sun et al. (2017) 7 showed that annual precipitation in China is projected to be approximately 2.5% higher under the 1.5 °C warming scenario compared with the present-day baseline (1980-2009).
These detailed explanations on the physical mechanisms behind the linear relationship between precipitation and temperature have been added in the revised version (see Lines 110-121 in the revised main text and Lines 357-374 in Method). Figure 1e, the authors showed a positive correlation between temperature anomaly and precipitation anomaly. I just wonder all models of CMIP6 showed the same relationship? It is possible that several models with strong relationship dominantly determines the overall relationship between temperature and precipitation over Asia. Also, the authors should clarify that such models with dominant relationships have better performances to simulate the Asian climate.

Response:
To address this query, we extracted future projections (2015-2100) of precipitation and temperature in Asia from each of the 27 CMIP6 models (see Supplementary Figure 6 in the revised SI), and found that almost all the models exhibit positive linear correlations between temperature and precipitation under all the SSPs (the only exception is the NorESM2-LM model which exhibits poor performance in reproducing historical precipitation under SSP126 -the correlation coefficient between simulated and observed precipitation during 1970-2015 is only of 0.09, and the P value is 0.56). The correlation coefficients are generally higher than 0.6 (P value<0.001), especially under SSP585. Therefore, our analysis does not support the assumption that only several models with strong relationships dominantly determine the overall relationship between temperature and precipitation over Asia. We have added text explaining that this is a consistent relationship across all CMIP6 models (see Lines 94-96 in the revised main text).

Comment 3.
The authors never mentioned how to calculate the area-mean values for Asia. This is significantly essential because it is possible that some regions dominantly determine the linear relationship between precipitation and temperature. In Supplementary Figures 2 and 3, warming tendency over Asia is more prominent in higher latitudes, while increasing precipitation is more robust in lower latitudes. Then, how can the authors explain the linear relationship between two variables for different regions of Asia? Response: We added the method for calculating the area-mean values for Asia as follows (see Lines 65-66 and 69-70 in the revised main text): The area-mean precipitation/temperature for the whole of Asia is calculated by averaging the values of all the grid cells, which is in agreement with other references using the emergent constraint method at global and continental scales [8][9][10][11] and other studies examining the sensitivity of precipitation, runoff, and evaporation [12][13][14][15] .
To respond to the referee's concern that some regions may dominantly determine the linear relationship between precipitation and temperature, we randomly selected eight square areas in Asia located at different latitudes (see Supplementary Figure 5 in the revised SI and Lines 91-94 in the revised main text), and found significant positive relationships during 1970-2014 in each of the sub-areas based on various observed datasets of precipitation (GPCC, 20CRv2c, HadCRUT4, GHCN, CMAP and ERA-Interim) and temperature (Delaware, HadCRUT4, GISS, NOAA) (R>0.54 P value<0.001). Furthermore, we examined the spatial distribution of the correlation coefficient during the future period (2015-2100) based on the CMIP6 projections, and found high positive correlation coefficients (R≥0.4 and corresponding P value<0.001) between temperature and precipitation in 82.0-92.1% of Asia, covering various latitudes (see Supplementary Figure 7 in the revised SI and Lines 96-97 in the revised main text). Therefore, the linear relationship is overall robust over Asia.
The referee is right that warming tendency over Asia is more prominent in higher latitudes with higher increasing rates of precipitation in Figs. S2 and S3. However, we should notice that, in a positive relationship, high values of one variable map high values of the other variable, and low values map low values. Consistently, in the lower latitudes of Asia where the warming tendency is relatively weak, the increasing rate of precipitation is also small. Situations in higher and lower latitudes of Asia are just the two sides of one coin.
The consistent strong positive relationships between precipitation and temperature across Asia further support the notion that it is reasonable to average the values of all the grid cells to calculate the mean values. We have added explanations to clarify the reasonability of our method (see Line 94 in the revised main text).

Comment 4.
The authors elucidated the change in precipitation using the energy budget equation. However, this equation only explains the local water cycle. In fact, the Asian climate is significantly affected by a number of climate factors such as monsoon, ENSO, and AO, which make the relationship between temperature and precipitation complicated. Response: The referee raised a key question how other climate factors, such as monsoons, ENSO and AO, etc. affect the relationship between temperature and precipitation by altering the likelihood and intensity of extreme climate events [16][17][18][19] . To address the referee's concern, we examined the precipitation-temperature relations using a moving average method with window lengths of 5-10 years in the revised manuscript, which significantly reduces the influence of large-scale climate variability and better reflects the long-term trend 20-21 . The results show that strong positive relations still exist between precipitation and surface air temperature after smoothing out extreme fluctuations (see Supplementary Fig. 8a in the revised SI), proving the reliability of the previously identified relationships. Furthermore, the sensitivity of precipitation to temperature change estimated by the new relationship remains (it is only slightly increased by 8.9-10.1%, see Supplementary Fig. 8b in the revised SI), implying that the effects of monsoons, ENSO and AO are not significant in this study. We added explanations in the revised manuscript (see Lines126-137 in the revised main text).

Comment 5.
To reduce the uncertainties of climate change projection, bias correction methods have been widely used. Then what are the advantages of the emergent constraint? Does the emergent constraint lead to better performance than bias correction? Response: This is a very interesting question which, to our knowledge, has not yet been discussed by any papers. Essentially, both approaches consider the difference between projections and observations; they both assume that the difference between projections and observations over a historical period is likely to be the same in the future. However, we think the major advantage of the emergent constraint method is that it is more physically-based than bias correction because it assumes that the physics (i.e., the relationship between different variables) remain the same in the historical and future periods, while most bias correction methods simply apply a "shift" to the data. In implementing the emergent constraint method, we cannot claim that we identify an emergent constraint relationship without the support of physical mechanisms, even though we find a tight relationship between the simulated historical changes of one climate variable and the projected future changes of another 22 . In contrast, bias correction methods have been developed to adjust or downscale simulated climate variables 23-24 based on correction factors that are obtained by simply exploring the statistical differences between simulations and observations. Without sufficient emphasis on the physical mechanisms, bias correction methods sometimes destroy the physical consistency among different climate variables, leading to failures in correcting the simulated results. For instance, temperature may become sub-zero after bias correction, but rainfall is not automatically converted into snowfall 25 . Thus, the emergent constraint method is more reliable than the bias correction methods. We have added comparisons between the two in the revised Method (see Lines 282-283) and Section 4 of the Supplementary Text in the revised SI.
Minor concerns: Comment 1. What is the latitude and longitude information for the Asian domain applied in this study? There is no information about this in the main text. Response: Thank you for your comment. We have added the coverage of Asia applied in this study in Fig. 1a   The land surface air temperature during 1970-2014 is very well simulated by the CMIP6 models relative to observations with an error of -0.01 (4.43 calculated from the average grid cell value of all raw CMIP6 model outputs across Asia, with no bias correction performed vs. 4.44 for the observational HadCRUT4 data set). In comparison, the discrepancy between the CMIP5 outputs and the observations is much higher (-0.34 ). Here we further estimated the mean absolute error, and found that the CMIP6 models still exhibit better performance with a mean absolute error of 1.52 than the CMIP5 models (mean absolute error of 1.77 ℃). Spatial distributions of the difference between the simulated and the observed historical temperature for CMIP6 (Supplementary Figure 2a) and CMIP5 (Supplementary Figure 2b) during the mutual historical period of CMIP5 and CMIP6 (i.e. 1986-2005) also show that the performance of the CMIP6 models is generally better than the CMIP5 outputs, especially in the Himalaya Mountains and North India.
In reproducing historical precipitation, although the mean bias of the CMIP5 models is smaller than that of the CMIP6 models (0.23 mm day -1 vs. 0.32 mm day -1 ), the performance of CMIP6 models is actually better than the CMIP5 models when comparing the mean absolute bias (0.432 mm day -1 vs. 0.441 mm day -1 ). Spatial distributions of the CMIP6-based difference between the simulated historical temperature and the observed one (Supplementary Figure 2c) and the CMIP5-based difference (Supplementary Figure 2d) during the mutual historical period of CMIP5 and CMIP6 (i.e. 1986-2005) also show that the performance of the CMIP6 models is generally better than the CMIP5 outputs, especially in the central and northern areas of India, the eastern area of Southeast Asia, and Southeast China.
Overall, the CMIP6 models have better performances in reproducing historical temperature and precipitation in Asia, because the latest generation of ESMs (CMIP6) has increased both the vertical and horizontal spatial resolutions in the models, and includes more comprehensive numerical experimental designs and more detailed processes descriptions.

Comment 4.
Line 132: What is EC? Does it mean the emergent constraint? Then use the full name. Response: Yes, EC stands for emergent constraint. We used the full name throughout the revised manuscript (Lines 145, 517, and 529). Thank you for your suggestion. Figures. 2-4, some regions have a negative relationship between temperature and precipitation (e.g., Pakistan and Indonesia). The authors should clarify whether such regions were included in the analysis or not. Response: As the referee pointed out, our study area included the regions presenting negative relationship between temperature and precipitation (Supplementary Figure  7), which may better reflect the complexity of the atmosphere-land-ocean interactions in Asia. However, these regions only occupy 7.9-18% (depending on the SSPs) of the total area of Asia, and we find that such a small percentage area does not affect the area-averaged emergent constraint relationship. In the revised manuscript, we discussed the inclusion of the regions with a negative relationship between temperature and precipitation, and we examined the emergent constraint relationship without these regions. We found that the positive emergent constraint relationships remained under almost all four SSPs with changes in the regression slopes of only 2.8-4.0% (Supplementary Figure 9), proving that the influence of such regions on the area-averaged emergent constraint relationship is relatively small (see Lines 141-142 in the revised main text and Section 2 of the Supplementary Text in the revised SI).

Comment 6.
Line 225-227: In Figure 3b, d, f, inter-model uncertainties decreased effectively after the emergent constraint. However, the minimum values of intermodel uncertainties of temperature and evaporation did not significantly change after the emergent constraint (Figure 3b, d). In case of the snow cover, the opposite occurred. Maybe only certain CMIP6 models are sensitive to the emergent constraint, resulting in these results. Therefore, the authors should investigate the sensitivity of each model to the emergent constraint. Response: In Figure 3b, d, f, the upper and lower lines of the colour histograms do not stand for the minimum/maximum values, but the mean ± one standard deviation. The referee also suggested that the selection of models might affect the variation range of different climate variables, which is very constructive. However, it is impossible to examine the sensitivity of individual models, because the emergent constraint relationship must be set up based on a set of models (taking Figure 2 for example, every circle stands for one model, and a regression line is derived based on all the circles.) Therefore, we try to analyse the effect of model selection by selecting the same models involved in developing the relationships between future total evaporation/snow cover fraction growth rates and future precipitation growth rates (listed in Supplementary Table 3), and derived new constraint relationships (see Supplementary Figure 24). The similarity between the results shown in Supplementary Figure 24b,d and Figure 3d,f suggest that the selection of models does not change the relative variation range of (Mean Value + one Standard Deviation) to that of (Mean Value -one Standard Deviation). We provided explanations in Lines 539-541 in the revised main text, and Section 3 of the Supplementary Text in the revised SI).

Comment 7.
Line 228-239: There are some snow-free regions in Asia (e.g., Southeast Asia near the equator), so the analysis region should narrow down when you calculate the relationship between snow cover fraction and temperature. Response: In this study, we focused purely on the regions with snow cover when constraining the future decreasing rate of snow cover fraction in Asia (see Fig. 3e and f in the revised main text). In the revised manuscript, we clarify that we have already excluded the snow-free regions (see Lines 537-538 in the revised main text).

Responses to Reviewer #2
Review for the paper entitled "Constrained CMIP6 projections indicate slower warming rates and reduced water availability across Asia" General Comments: The paper is well written and clear on the results. The methodology is explained in detail with all information needed. The findings are significant and seem supported by the figures, but I have a main major concern about their interpretation. Response: Thank you very much. We have carefully revised the manuscript according to the referee's comments, which were very valuable for improving the interpretation of the findings.

Comment 1.
Most of the emergent constraint signal is claimed to be related to precipitation feedback on temperatures. However, by reading the picture my first conclusion would be that models warming the most also see the largest increase in precipitation simply because of thermodynamics laws (higher temperature = more evaporative world). For me it's not really clear that there is a feedback here. Maybe one thing to do would be to express the precipitation change per °C (instead of per year). That's my only major concern about the paper but I think it really needs to be clarified (either by clearly showing how it's a feedback and not just thermodynamics, or by rephrasing the text and discussion around thermodynamics considerations). It would probably not change the main results (the relation between model warming the most and having more precipitation would still be the same), but it must be clear why it is so.

Response:
We agree with the referee that our findings are mostly due to the thermodynamics. We have clarified this in the revised version and rephrased the text throughout (Lines 119, 172, 313 in the revised main text). We have also expressed the precipitation change per °C in addition to the change per year (Please see Lines 9-11 and 167-171 in the revised main text).

Some other suggestions:
Comment 1. Line 65: "Asia" domain should be defined here maybe? Response: Thank you for your comment. We have shown the coverage of Asia in this study in Fig. 1a in the revised main text. Supplementary Figures 2 and 7 1 . We generated the cumulative distributions of the future precipitation growth rate before and after application of the emergent constraint (Supplementary Figure 11 in the revised SI), calculated the K-S statistics (See Supplementary Table 9 in the revised SI), and found the shifts are significant under a confidence level of 95% (all the K-S statistics are higher than the critical value at the 95% confidence level). We added relevant text in Lines 166-167 in the revised main text.  Figure 18 in the revised SI). In addition, we also explored the potential emergent constraint relationships between historical trends in relative humidity/soil water content/land surface runoff and future annual precipitation growth rates across the CMIP6 models (see Lines 185-187 in the revised main text and Supplementary Figures 19 to 21 in the revised SI).
Comment 5. L191-195: Instead of constraining the future temperatures based on a constrained precipitation why not simply constrain future T based on historical T? Response: Thank you for your suggestion. We set up the emergent constraint relationship between the annual growth rates of the historical temperature and the future temperature across 23 CMIP6 models (Supplementary Figure 23a), and explained the physical mechanisms as follows: There exists a proportionally positive feedback in temperature to the rising radiative forcing, i.e., past and future warming trends are both controlled by the sensitivity of such feedback 2 . Thus, the future warming trends are firmly linked with the historical temperature growth rate which can be used to constrain the future temperature growth rate. This mechanism has been widely applied to constrain equilibrium climate sensitivity (ECS), transient climate response (TCR) and ocean heat uptake 2,3-7 (see Lines 215-221 in the revised main text).
The constrained results by using past warming trends are highly consistent with our original conclusions (see Supplementary Figure 23b and c, and Lines 221-227 in the revised main text). Comment 6. Fig.1c: It would be nice to add some robustness/uncertainty on OBS trends (by bootstrapping the sampling for example and recomputing the trend...) General Comments: With a similar approach done by Chai et al. (2021) for the Amazon dieback, this manuscript investigated historical temperature and precipitation trends in Asia by CMIP6 models against the observations, and used the results to adjust future projections. As CMIP6 models overestimate historical precipitation changes during 1970-2014, future precipitation projections are downgraded. However, the reviewer has some concerns. Response: Thank you for your helpful comments which were very valuable for improving the manuscript. We have carefully revised the manuscript to address each of the referee's concerns. Comment 1. First, the emergent constraint seeks physical mechanism of a possible relationship between the two variables, but this approach will not work well in this subject, because regional precipitation is not governed by temperatures only, but also much influenced by circulation changes and associated moisture convergence. Response: We agree with the referee that it is important to assess the degree to which changes in regional precipitation are governed by temperature changes vs circulation changes and associated moisture convergence. To examine whether the influence of climate variability (such as the monsoon, ENSO, AO, etc.) alters the thermodynamic precipitation-temperature relationship in different regions of Asia on annual timescales, first, we randomly selected eight square areas of Asia located at different latitudes (see Supplementary Figure 5 in the revised SI and Lines 91-94 in the revised main text), and found that the significant positive relationships during 1970-2014 were consistent in each of the sub-areas based on various observed datasets of precipitation (GPCC, 20CRv2c, HadCRUT4, GHCN, CMAP and ERA-Interim) and temperature (Delaware, HadCRUT4, GISS, NOAA). Furthermore, we examined the spatial distribution of the correlation coefficient during the future period (2015-2100) based on the CMIP6 projections, and found high positive correlation coefficients (R≥ 0.4 and corresponding P value<0.001) between temperature and precipitation across 82.0-92.1% of Asia (see Supplementary Figure 7 in the revised SI and Lines 96-97 in the revised main text). Therefore, the linear relationship is overall robust over Asia, and the thermodynamic effect is equally important across the whole of Asia.
Second, considering that circulation changes, such as monsoons, ENSO and AO, etc. usually affect the relationship between temperature and precipitation by increasing the likelihood and intensity of extreme weather events 1-4 , we used the moving average method with window lengths of 5-10 years to examine the precipitation-temperature relations. With this method, the influence of large-scale climate variability is significantly reduced and the long-term trend is better reflected [5][6] . The results show that strong positive relations still exist between precipitation and surface air temperature after smoothing out extreme fluctuations (see Supplementary  Figure 8a in the revised SI), proving the reliability of the previously identified relationships. Furthermore, the sensitivity of precipitation to temperature change estimated by the new relationship remains (it is only slightly increased by 8.9-10.1%, see Supplementary Figure 8b in the revised SI), implying that the effects of monsoons, ENSO and AO are not significant in this study. We added relative explanations in the revised manuscript (see Lines 126-137 in the revised main text).
Finally, we provided further evidence to support the linear relationships by collecting additional observed datasets of precipitation (GPCC, 20CRv2c, HadCRUT4, GHCN, CMAP and ERA-Interim) and temperature (Delaware, HadCRUT4, GISS, NOAA) in Asia during 1970-2014, and by extracting future projections (2015-2100) of precipitation and temperature in Asia for each of the 27 CMIP6 models. Consistently, significant linear relationships have been identified among all the datasets (see Supplementary Figure 4 in the revised SI and Fig.1e in the main text and Lines 87-91 in the revised main text) and in almost all the models under the four SSPs (see Supplementary Figure 6 in the revised SI and Lines 94-96 in the revised main text). The only exception is the NorESM2-LM model which exhibits poor performance in reproducing historical precipitation under SSP126 (the correlation coefficient between simulated and observed precipitation during 1970-2015 is only of 0.09, and the P value is 0.56). In addition, in-depth explanations for the physical mechanisms behind the constraint relationship have been added (see Lines 110-121 in the revised main text and Lines 357-374 in Method).

Comment 2.
Second, the authors adjust future precipitation changes in the models in which historical temperature growth rate is large, although the ensemble mean historical temperature trend fits the observation very well. Response: We added a new figure (see Supplementary Figure 10 in the revised SI) to demonstrate that even if the ensemble mean historical temperature trend fits the observations very well, the constrained future precipitation may still differ from the raw projections with different levels of uncertainty. This is mainly due to different probability distributions of observational temperature and simulated temperature. We clarified this in Lines 150-153 in the revised main text. Comment 3. Third, after reducing the future precipitation trends, authors decrease the future temperature trends, although models had no significant bias in their historical period. The reviewer is not confident with the authors hypotheses. Response: Indeed, the mean temperature of the models shows no significant bias against observations in the historical period. However, individual models may still perform poorly (see Supplementary Figure 22 in the revised SI and Lines 196-199 in the revised main text), leading to large uncertainties in simulating the temperature growth rate in both the historical and the future periods (see Fig. 1b). Therefore, it is legitimate to wish to constrain the model projections.
To further verify the constrained results of the future temperature growth rate, we set up an emergent constraint relationship between the annual growth rates of the historical temperature and the future temperature across 23 CMIP6 models (Supplementary Figure 23a), considering the firm link between the past and future warming trends (Tokarska et al., 2020 7 ). The physical mechanism behind the potential constrained relationships is as follows: There exists a proportionally positive feedback in temperature to the rising radiative forcing, i.e., the past and future warming trends are both controlled by the sensitivity of such feedback 2 . Thus, the future warming trends are firmly linked with the historical temperature growth rate, which can be used to constrain the future temperature growth rate. This mechanism has been widely applied to constrain equilibrium climate sensitivity (ECS), transient climate response (TCR) and ocean heat uptake [8][9][10][11] (see Lines 215-221 in the revised main text).
The new constrained results are highly consistent with our original conclusions (see Supplementary Figure 23b and c, and Lines 221-227 in the revised main text).
Other comments Comment 1. Methods for calculation are missing. How are different horizontal resolutions of observations and models treated? Which is the area of Asia? Response: Thank you for your comments. We re-gridded all the CMIP6 output layers and the observational data sets to a uniform 0.25 o ×0.25 o latitude-longitude spatial resolution for calculating the multi-model mean values (see Lines 348-350 in the revised Data Availability section). Additionally, we have added the coverage of Asia applied in this study in Fig. 1a in the revised main text. Supplementary Figures 2 and  7 in the updated SI are also replaced with the Asian domain versions. . However, other studies reported that El Nino-like mean SST changes will also bring large effects (Martins et al., 2015) 15 . In the revised manuscript, we have added discussions on the effects of El Nino-like mean SST changes on precipitation in Amazon (see Lines 181-182 in the revised main text). Table 1 and 2? Captions and contents are same. Response: Thanks for pointing this out. We have removed the Supplementary Table 2 in the revised SI.

Comment 3. What is the difference between Supplementary
The authors properly revised the manuscript according to my comments. Therefore, it is acceptable for the publication in Nature Communications.
Reviewer #2 (Remarks to the Author): Authors have respond clearly to all my comments and updated the manuscript accordingly. Thus I find it suitable for publication.
Reviewer #3 (Remarks to the Author): I still have the same comments raised to the original manuscript. In particular, I do not agree applying an emergent constraint between temperature and precipitation to future regional precipitation changes in Asia because many factors other than thermal conditions would work on regional precipitation changes. Also, future temperature constraint is not understandable because "the mean temperature of the models shows no significant bias against observations in the historical period". The reviewer considers that a rebuttal on these points has not been properly made.

Responses to Reviewers #1 and #2
Reviewer #1 (Remarks to the Author): The authors properly revised the manuscript according to my comments. Therefore, it is acceptable for the publication in Nature Communications.
Reviewer #2 (Remarks to the Author): Authors have responded clearly to all my comments and updated the manuscr ipt accordingly. Thus, I find it suitable for publication.
Response: Thank you very much for your constructive comments and suggestions in the previous round. In this round, we believe we have fully addressed your further concerns about the physical mechanisms behind the emergent constraint between temperature and precipitation in Asia. Please refer to our detailed responses to the Editor and Reviewer #3.

Responses to Reviewer #3
Comment 1: I still have the same comments raised to the original manuscript. In particular, I do not agree applying an emergent constraint between temperature and precipitation to future regional precipitation changes in Asia because many factors other than thermal conditions would work on regional precipitation changes.
Response: As the referee rightly points out, it is fundamentally important to confir m that the emergent relationship between the growth rates of temperature and precipitatio n arises from physical processes, rather than emerging by chance, especially at the (1) Plausible mechanisms.
The referee points out that many factors other than thermal conditions would affect regional precipitationwhich is entirely reasonable. Previous studies mainly classified factors affecting precipitation into 'dynamic' and 'thermodynamic' categories (Emori Then, we also test the CAPE relationship with annual precipitation in Asia during 1979-2014, and again find poor correlation ( Figure R4, r=-0.24, p>0.1). These results imply that 'dynamic' factors do not strongly affect long-term mean precipitation over the large area considered in our study.  Taking the reviewer's comments fully into consideration, we also analyze whether the relationship between the growth rates of simulated historical temperature and projected future precipitation in Asia is significantly affected by regions experienc ing strong atmospheric circulation. According to Van der Ent et al. (2010) 10 , precipitatio n in regions with low continental precipitation-recycling ratio (ρc, defined as the ratio of precipitation of continental origin [not necessarily from the same continent] to that of both continental and oceanic origin) primarily derives from moisture transport from the oceans. Here we selected areas with ρc < 0.5 in Asia as regions subject to monsoons and ENSO events (such as southeastern China, etc.). By examining the relationship between the growth rates of simulated historical temperature and projected future precipitatio n when excluding regions of low ρc, we found that the linear regression results remain almost unchanged under all four shared socioeconomic pathways (SSPs) (i.e., changes in the regression slope are only 0.2-16.0%, see Figure R5). This implies that such regions with strong atmospheric circulation in Asia do not affect the overall relations hip between the long-term mean growth rates of precipitation and temperature in Asia. A similar analysis using a moving average method with window lengths of 5-10 years to exclude extreme precipitation mainly driven by monsoons and ENSO events was conducted in the previous round of revision. The findings were similar in that strong positive relations persist (with slight increases by 8.9-10.1%, see Figure R6) between precipitation and surface air temperature after smoothing out extreme fluctuations. These again support the physical hypothesis that precipitation change in Asia is not so affected by monsoons and ENSO events.  (2) Out-of-sample testing.
Hall et al. (2019) 1 pointed out that testing the emergent constraint relations hip using other ESM ensembles is an indirect but effective way to improve the reliability of introduced emergent constraints because it is equivalent to enlarging the origina l ensemble. Provided high correlation persists, the likelihood that the emergent relationship has emerged by chance is then greatly reduced. We therefore also tested the emergent relationships in the CMIP5 models. As shown in Figure R7, the relationship between temperature and precipitation also exists across CMIP5 models achieving high correlation (r=0.72, p value<0.001). We added relevant contents in Lines 139-142 in the main text, and Supplementary Fig. 13. constraint) can ever be completely confirmed and is instead associated with degrees of confirmation." We believe that the degree of confirmation of our emergent constraint relationship is already very high, compared to that of other emergent constraint papers.

Comment 2:
Also, future temperature constraint is not understandable because "the mean temperature of the models shows no significant bias against observations in the historical period". The reviewer considers that a rebuttal on these points has not been properly made.
Response: Thank you for pointing this out. The reviewer is correct that the multi-mod e l mean value of annual average land surface air temperature in Asia (4.43 ℃) shows no significant bias against observations (4.44 ℃) during 1970-2014. However, in our case, we try to bring a constraint on annual growth rate in temperature, rather than the mean temperature. In fact, the multi-model mean annual growth rate in temperature (0.363 ± 0.0732 ℃ decade -1 ) has non-negligible bias in comparison with observations (0.326 ± 0.035 ℃ decade -1 ); the simulated temperature growth rate is therefore overestima ted by 11.35%. Probability density distributions of annual growth rates in temperature based on observations (red line in Figure R8) and the CMIP6 multi-model mean values (black line in Figure R8) also exhibit large discrepancy. Such obvious bias indicates the necessity to bring a constraint on future temperature growth rate. The constrained results of future temperature growth rate also exhibit an overestimate of 3.4-11.6% compared with the raw projection.
To avoid confusion, we have included a discussion of the discrepancy between the observed and simulated temperature growth rates in the revised manuscript (see Lines 193-199 in the main text).

REVIEWERS' COMMENTS
Reviewer #2 (Remarks to the Author): I think the authors have made a significant effort to answer all comments from Reviewer 3. It seems for me that their analysis is convincing and justified enough to be published.
Reviewer #3 (Remarks to the Author): I appreciated further analysis made by authors on relative importance between thermodynamic and dynamic contribution on future mean precipitation changes. My impression from Figure R3 is that dynamic factor with r ~ 0.5 may not be neglected. They may be significant at 95% level. I wish the authors make the dynamic attributions in their future work. As this is reminded explicitly in the revised main text and further evaluation of this paper will take place once it is made public, I agree on a publication of this manuscript.

Reviewer #2 (Remarks to the Author):
Comment: I think the authors have made a significant effort to answer all comments from Reviewer 3. It seems for me that their analysis is convincing and justified enough to be published.
Response: Thank you very much for reviewing our manuscript. Your comments during the whole process helped to improve our paper considerably.

Reviewer #3 (Remarks to the Author):
Comment 1: I appreciated further analysis made by authors on relative importance between thermodynamic and dynamic contribution on future mean precipitation changes.

Response:
The authors appreciate the reviewer's comments during the whole review process, especially the one concerning the impact of dynamic factors which could be negligible at regional scale. By addressing your previous concerns, our study has become more convincing. Figure R3 is that dynamic factor with r ~ 0.5 may not be neglected. They may be significant at 95% level. I wish the authors make the dynamic attributions in their future work. As this is reminded explicitly in the revised main text and further evaluation of this paper will take place once it is made public, I agree on a publication of this manuscript.

Response:
The reviewer is right that dynamic factors with r ~ 0.5 may be significant at the 95% level and must be assessed in future work. Thus, for clarity, in the revised manuscript, we indicate on the figure panels (see Supplementary Fig. 8) whether the correlations between pressure vertical velocity at 11 pressure levels and precipitation are significant at the 95% level (0.01 < p value < 0.05), or not (p value > 0.05). We changed Lines 141-143 and 146-147 to "we found that the dynamic factors exhibit some correlation with the long-term trend in precipitation in continental Asia (-0.46<r<-0.24), but not so strong as the thermodynamic factors … However, the contribution of dynamic factors will be assessed in future work", and Lines 290-295 to "Although thermodynamic factors have been widely recognized as playing the lead role in driving changes in long-term mean precipitation over large areas 65-66 (while vertical pressure velocity and CAPE have smaller correlation coefficients), dynamic factors may still be significant ( Supplementary Fig. 8) under certain circumstances. Therefore, it would be worthwhile to determine the specific contributions of the dynamic factors to the long-term trend in precipitation change at the continental scale in future work."